Transcendental and mathematical infinity in Kant's first antinomy

Abstract

ABSTRACT Kant's first antinomy uses a notion of infinity that is tied to the concept of (finitary) successive synthesis. It is commonly objected that (i) this notion is inadequate by modern mathematical standards, and that (ii) it is unable to establish the stark ontological assumption required for the thesis that an infinite series cannot exist. In this paper, I argue that Kant's notion of infinity is adequate for the set-up and the purpose of the antinomy. Regarding (i), I show that contrary to appearance, the Critique can even accommodate a modern notion of infinity without consequences for the antinomy; and regarding (ii), that the ‘ontological’ consequence indeed follows once its covertly epistemic character is adequately understood.